A090773 Numbers that are congruent to {4, 6} mod 10.

4, 6, 14, 16, 24, 26, 34, 36, 44, 46, 54, 56, 64, 66, 74, 76, 84, 86, 94, 96, 104, 106, 114, 116, 124, 126, 134, 136, 144, 146, 154, 156, 164, 166, 174, 176, 184, 186, 194, 196, 204, 206, 214, 216, 224, 226, 234, 236, 244, 246, 254, 256, 264, 266, 274, 276, 284

Offset: 1

Author

Giovanni Teofilatto, Feb 07 2004

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A047221, A090298, A179290, A300074.

Programs

Mathematica

#+{4,6}&/@(10Range[0,50])//Flatten (* or *) LinearRecurrence[{1,1,-1},{4,6,14},100] (* Harvey P. Dale, Jun 05 2017 *)

Formula

a(n) = 2 * A047221(n) = 5*n-5/2-3*(-1)^n/2.

a(n) = 10*n-a(n-1)-10 (with a(1)=4). - Vincenzo Librandi, Nov 16 2010

G.f.: 2*x*(2+x+2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/10. - Amiram Eldar, Dec 28 2021

From Amiram Eldar, Nov 23 2024: (Start)

Product_{n>=1} (1 - (-1)^n/a(n)) = cosec(2*Pi/5) (A179290).

Product_{n>=1} (1 + (-1)^n/a(n)) = cosec(Pi/5)/2 (A300074). (End)

Extensions

Edited and extended by Ray Chandler, Feb 10 2004